SEOUL — South Korea’s military warned Wednesday that it would respond to any attack from North Korea with “strong and stern measures” against Pyongyang’s top leadership, a particularly vivid threat that comes after the North vowed to nullify the armistice agreement ending the Korean War.

The tit-for-tat threats could prove to be mere bluster, analysts said. But the rhetoric sets up an especially tense period on the Korean Peninsula, with the U.S. and South Korean militaries planning joint training drills that the North considers a “dangerous nuclear war” maneuver, and with the U.N. Security Council deliberating new sanctions to limit Pyongyang’s weapons program.

The North said Tuesday that it will “completely declare invalid” the armistice on March 11, the day those joint drills enter the “full-dress stage.” The United States and South Korea began a two-month series of war exercises Friday, but an additional set of exercises — the Key Resolve drills, involving 10,000 South Korean and 3,500 U.S. troops — kicks off Monday.

South Korea typically shrugs off rhetoric from North Korea, but on Wednesday its Joint Chiefs of Staff released a statement saying the South would respond to provocations by striking “not only at the origin of provocation [and at] supporters of the provocation but also the top operatives.”

North Korea has started submarine drills of its own, a first step before nationwide military drills begin next week, South Korea’s Yonhap news agency reported, quoting unnamed military officials.

In its statement Tuesday, published in state media and attributed to the Supreme Command of the Korean People’s Army, the North threatened to cut off a hotline at the Demilitarized Zone. The statement also criticized the United States and South Korea for their effort to “slap” tougher sanctions on the North after the police state’s Feb. 12 underground nuclear test.

The latest round of sanctions is expected to be announced Thursday, after an apparent agreement between diplomats from the United States and China, the North’s main economic benefactor and trade partner.

North Korea’s latest threats “are consistent with previous . . . behavior and are meant to intimidate the United Nations Security Council as it deliberates on additional sanctions against Pyongyang,” Bruce Klingner, a senior researcher at the Heritage Foundation, wrote in an issue brief.